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Byju's Answer
Standard X
Mathematics
Rational Numbers
Prove that 2+...
Question
Prove that
2
+
3
is irrational.
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Solution
Let
(
2
+
3
)
be rational.
Then, both
(
2
+
3
)
and 2 are rational.
∴
{
(
2
+
3
)
-
2
}
is rational [∵ Difference of two rational is rational]
⇒
3
is rational.
This contradicts the fact that
3
is irrational.
The contradiction arises by assuming
(
2
+
3
)
is rational.
Hence,
(
2
+
3
)
is irrational.
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